Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Multiplying by 10 makes every digit worth ten times as much, so every digit moves one place to the left. Multiplying by 100 moves them two places and by 1,000 three places. With whole numbers, this shows up as zeros appearing at the end: 36 × 1,000 = 36,000. With decimals, the same shift makes it look as if the decimal point has jumped: 3.6 × 100 = 360. Dividing by a power of 10 shifts the digits the other way, so 45 ÷ 100 = 0.45.
Fifth graders also meet exponent notation for powers of 10. Writing 10³ is a short way to say 10 × 10 × 10, and the exponent tells how many factors of 10 there are, which matches the number of places the digits shift. Students should be able to explain the pattern rather than chant 'add a zero', because that slogan fails with decimals: 2.5 × 10 is 25, not 2.50.
This rule works for whole numbers but not decimals. 0.4 × 10 written as 0.40 has not changed in value. The digits must shift one place to the left, giving 4.
Students sometimes treat the exponent as a factor and get 30. Writing out 10 × 10 × 10 = 1,000 a few times corrects this.
Dividing by 100 makes a number smaller, so digits move to the right. A quick size check (should the answer be bigger or smaller?) catches this.
Students confuse 10² with 1,000. Linking the exponent to the number of zeros in the whole-number power (10² = 100 has two zeros) helps.
Find 0.075 × 10² and 830 ÷ 10³. Explain how the digits move.
Answer: 0.075 × 10² = 7.5 and 830 ÷ 10³ = 0.83.
A sliding place value chart, where the digits are on a strip that slides under fixed column headings, shows that the digits move while the decimal point stays put. This is more accurate than saying the decimal point moves, and it explains both the zeros pattern and the decimal pattern with one picture.
Expect items that give a product such as 4.3 × 10³ and ask for its value, ask for the missing exponent, or ask students to explain a pattern in a table of products.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 52000 (also accepted: 52,000)
Multiplying by 1,000 moves every digit three places to the left, so three zeros appear: 52,000.
Answer: 370
Each digit moves two places to the left: 3.7 becomes 370.
Answer: C) 10,000
10⁴ = 10 × 10 × 10 × 10 = 10,000, which has four zeros.
Answer: 0.64
Dividing by 100 moves each digit two places to the right: 64 becomes 0.64.
Answer: 1000 (also accepted: 1,000, 10³)
The digits moved three places to the left, so the factor is 1,000, which is 10³.
Answer: 0.92
Dividing by 10 moves each digit one place to the right, giving 0.92.
Answer: C) 6
Writing a zero on the end does not change 0.6. Multiplying by 10 moves the 6 from the tenths place to the ones place, so the answer is 6.
A full lesson with slides, activities and an exit ticket on powers of 10 and exponents, pitched to grade 5 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 5.NBT.A.2 with an answer key, ready in about a minute.
Make a worksheet →Turn powers of 10 and exponents into a quiz students answer online that marks itself, with a class summary for you.
Build a test →No. 5.NBT.A.2 only asks for whole-number exponents on powers of 10. General exponents such as 2³ are introduced in sixth grade.
It is a common shortcut, but it is more accurate to say the digits shift places while the decimal point stays fixed. The digit-shift explanation also matches what students learned about place value.